SOLUTION: Someone, PLEASE HELP, this is a problem i have never seen before. i would appeciate any help just to get started. Evaluate P(-1/2) if P(x) = 2x4 + x3 + 12

There are two methods to find 

First method:  by straight-forward plugging in  for x












Second method:  by synthetic division and the remainder
theorem which says that you get the same answer when you

1. plug a number directly into a polynomial 

as you get when you

2. write that number to the left of a synthetic division,
do the synthetic division, and take only the remainder,
which is the rightmost number on the bottom line of the
synthetic division. 

Notice that since the  and  terms are 
missing in the original polynomial, we have to insert
0's for them as placeholders:

 | 2    1    0    0   12
     |     -1    0    0    0
      ----------------------
       2    0    0    0   12

The last number on the right  is the remainder
which by the remainder theorem is 


Edwin